Also, a couple notes about the use of standard deviation (and general stuff
about benchmarking):
1. It is *vital* to keep in mind the distinction between a "sample
statistic" and a "population statistic". A sample statistic is a statistic
derived from the dataset of measured values, while a population statistic
is a mathematical function of the underlying probability distribution of
the phenomenon (some abstract "population" of possibilities) being sampled.
2. As you take more measurements, the standard deviation sample statistic
converges to the standard deviation population statistic regardless of the
underlying population distribution.
3. *Every* probability distribution has a defined standard deviation (it is
just a mathematical function of the distribution). For a Gaussian
distribution, the standard deviation (in conjunction with the mean)
completely describes the probability distribution. This is emphatically
*not* the case for all probability distributions [1]. In order to derive
insight from a standard deviation sample statistic, you *must* a priori
have a good reason to believe that the underlying probability
distribution's standard deviation provides useful information about the
actual distribution.
4. Any probability distribution can be made to have any standard deviation
without changing its distribution shape (technically, at most a linear
transformation of the coordinate is needed). To pick a random example, for
a highly bimodal distribution the standard deviation doesn't really give
you any useful information about the overall shape (and it doesn't exactly
correspond between the spacing between the modes either).
5. The standard deviation is nothing more than a root-mean-square average.
Basically, it is a very popular statistic because there is an *extremely
powerful* way to model phenomena for which the root-mean-square average is
the actual meaningful value that ties into the model. The theory I'm
talking about is used extensively in almost every science and engineering
discipline *outside of* software engineering (and the purely digital part
of hardware) [2]. Since this modeling technique is rarely directly relevant
in software, there is little reason to assume that the standard deviation
is a good statistic (there may be a good reason to, but I haven't seen
one).
Okay, so I've cast doubt on the use of standard deviation (and actually an
argument could be made against the mean too for similar reasons). On a more
constructive note, what *is* a good small set of parameters to summarize
measurements of program run time? One interesting model that was brought to
my attention by Nick Lewycky is based on the following observation: most
"perturbations" of the run time of a fixed program binary on a fixed chip
and fixed OS are due to externalities that contend for (or otherwise
deprive the program of) execution resources and therefore almost always
make it *slower*.
The model is then that there is a "true" execution time for the program,
which is a completely deterministic function of the program, chip, and OS;
intuitively, this is time occurs when the program is e.g. able to execute
by itself, on a single execution unit of the CPU, with no interrupts
knocking it off CPU, and no other threads using any of the execution
resources of this CPU. On top of this, we assume that there is a set of
perturbations that contend for execution resources and slow the program
down.
For this model, it makes sense to approximate the "true" value by the
maximum of the recorded values. If we want to use two numbers to summarize
the data, it probably makes sense to look at a way of characterizing the
extent of the variation from this "true" value. In the absence of proper
characterization of the perturbations (such as the distribution of when
they occur and how much effect they have when they occur), one simple
solution is the minimum. Max and min might be *too* sensitive to the
perturbations (especially disk cache of the program itself on the first
run), so a pair of percentiles might be a bit more reliable, such as 10th
percentile and 90th percentile.
Next time I'm measuring program run time, I'm going to try out this model.
It should be possible to look at a higher-degree-of-freedom representation
of the dataset, like a histogram of the distribution, in order to evaluate
how well this two-parameter characterization of the data works compared
with the typical mean and stddev. Also, ultimately we only need as much
precision here as is necessary for what we are doing with the summarized
data, which typically is to alert us of a significant change. On a
sufficiently quiet machine, the variance of the measurements might be
significantly smaller than the thresholds that we consider "significant" so
that the mean, median, max, min, 10%-ile etc. are all so close that it does
not matter which we use, and we can summarize the data with just a single
number, which can be any one of them (and just trigger an error if total
variation exceeds a set amount).
However, the noisier the machine (and hence our data), the more important
is is to properly model and analyze things to avoid coming to a faulty
conclusion (note: reliable conclusions can be made from data with large
amounts of noise as long as there is a good model which allows isolating
the data we are interested in from the noise [3]).
Nick, I forget from when we talked, but did you guys ever settle on a model
like this for your internal benchmarking?
[1] If you are familiar with Fourier theory, using only two statistics to
describe a probability distribution is sort of like using only two Fourier
components to describe a function. In order to conclude *anything* you must
a priori know that the other components are not important!
[2] The modeling technique I'm talking about is decomposition of
square-integrable function spaces into an orthonormal basis (this is by no
means the most general way of describing the idea). This is a far-reaching
concept and pops up under many names. Things like "frequency domain",
"Fourier transform", "Laplace transform", and "spectrum" are among the most
elementary. More advanced ones are "wavelets", "Hilbert space",
"eigenfunctions of a linear operator". A smattering of use cases:
determining the shape of the electron orbitals of hydrogen, designing the
fuel control system of a jet engine to make sure the right amount of fuel
is being provided at any given moment, designing the circuits sitting at
the end of a communication line (or a cell phone antenna) that have to
detect incoming signals with the least chance of error, analyzing the
structure of molecules based on X-ray diffraction, determining the chemical
composition of the atmosphere of a planet orbiting another star.
[3] For example if you know that there is Gaussian noise (even a very large
amount) on top of an underlying value, then the underlying value is just
the mean of the population (which will be a Gaussian distribution) and can
be reliably determined from the mean sample statistic.
On Thu, Dec 18, 2014 at 4:10 AM, Sean Silva wrote:
>
> In the future could you please do some sort of visualization of your
data,
> or at least provide the raw data in a machine-readable format so that
> others can do so?
>
> It is incredibly easy to come to incorrect conclusions when looking at
> lists of numbers because at any given moment you have a very localized
view
> of the dataset and are prone to locally pattern-match and form a
selection
> bias that corrupts your ability to make a proper decision in the context
of
> the entire dataset. Even if you go on to look at the rest of the data,
this
> selection bias limits your ability to come to a correct "global"
conclusion.
>
> Appropriate reliable summary statistics can also help, but are not
> panacea. In using, say, 2 summary statistics (e.g. mean and standard
> deviation), one is discarding a large number of degrees of freedom from
the
> dataset. This is fine if you have good reason to believe that these 2
> degrees of freedom adequately explain the underlying dataset (e.g. there
is
> a sound theoretical description of the phenomenon being measured that
> suggests it should follow a Gaussian distribution; hence mean and stddev
> completely characterize the distribution). However, in the world of
> programs and compiler optimizations, there is very rarely a good reason
to
> believe that any particular dataset (e.g. benchmark results for SPEC for
a
> particular optimization) is explained by a handful of common summary
> statistics, and so looking only at summary statistics can often conceal
> important insights into the data (or even be actively misleading). This
is
> especially true when looking across different programs (I die a little
> inside every time I see someone cite a SPEC geomean).
>
> In compilers we are usually more interested in actually discovering
*which
> parameters* are responsible for variation, rather than increasing
> confidence in the values of an a priori set of known parameters. E.g. if
> you are measuring the time it takes a laser beam to bounce off the moon
and
> come back to you (in order to measure the distance of the moon) you have
an
> a priori known set of parameters that well-characterize the data you
> obtain, based on your knowledge of the measurement apparatus, atmospheric
> dispersion, the fact that you know the moon is moving in an orbit, etc.
You
> can perform repeated measurements with the apparatus to narrow in on the
> values of the parameters. In compilers, we rarely have such a simple and
> small set of parameters that are known to adequately characterize the
data
> we are trying to understand; when investigating an optimization's
results,
> we are almost always investigating a situation that would resemble (in
the
> moon-bounce analogy) an unknown variation that turns out to be due to
> whether the lab assistant is leaning against the apparatus or not. You're
> not going to find out that the lab assistant's pose is at fault by
looking
> at your "repeatedly do them to increase confidence in the values"
> measurements (e.g. the actual moon-bounce measurements; or looking at the
> average time for a particular SPEC benchmark to run); you find it by
> getting up and going to the room with the apparatus and investigating all
> manner of things until you narrow in on the lab assistant's pose (usually
> this takes the form of having to dig around in assembly, extract kernels,
> time particular sub-things, profile things, look at what how the code
> changes throughout the optimization pipeline, instrument things, etc.;
> there are tons of places for the root cause to hide).
>
> If you have to remember something from that last paragraph, remember that
> not everything boils down to click "run" and get a timing for SPEC. Often
> you need to take some time to narrow in on the damn lab assistant.
> Sometimes just the timing of a particular benchmark leads to a "lab
> assistant" situation (although hopefully this doesn't happen too often;
it
> does happen though: e.g. I have been in a situation where a benchmark
> surprisingly goes 50% faster on about 1/10 runs). When working across
> different programs, you are almost always in a "lab assistant" situation.
>
> -- Sean Silva
>
> On Mon, Dec 15, 2014 at 11:27 AM, Daniel Stewart
> wrote:
>
>> I have done some preliminary investigation into postponing some of the
>> passes to see what the resulting performance impact would be. This is a
>> fairly crude attempt at moving passes around to see if there is any
>> potential benefit. I have attached the patch I used to do the tests, in
>> case anyone is interested.
>>
>>
>>
>> Briefly, the patch allows two different flows, with either a flag of
>> –lto-new or –lto-new2. In the first case, the vectorization passes
are
>> postponed from the end of populateModulePassManager() function to midway
>> through the addLTOOptimizationPasses(). In the second case, essentially
the
>> entire populateModulePassManager() function is deferred until link time.
>>
>>
>>
>> I ran spec2000/2006 on an ARM platform (Nexus 4), comparing 4
>> configurations (O3, O3 LTO, O3 LTO new, O3 LTO new 2). I have attached a
>> PDF presenting the results from the test. The first 4 columns have the
spec
>> result (ratio) for the 4 different configurations. The second set of
>> columns are the respective test / max(result of 4 configurations). I
used
>> this last one to see how well/poor a particular configuration was in
>> comparison to other configurations.
>>
>>
>>
>> In general, there appears to be some benefit to be gained in a couple of
>> the benchmarks (spec2000/art, spec2006/milc) by postponing
vectorization.
>>
>>
>>
>> I just wanted to present this information to the community to see if
>> there is interest in pursuing the idea of postponing passes.
>>
>>
>>
>> Daniel
>>
>>
>>
>> *From:* [email protected] [mailto:[email protected]]
*On
>> Behalf Of *Daniel Stewart
>> *Sent:* Wednesday, September 17, 2014 9:46 AM
>> *To:* [email protected]
>> *Subject:* [LLVMdev] Postponing more passes in LTO
>>
>>
>>
>> Looking at the existing flow of passes for LTO, it appears that most all
>> passes are run on a per file basis, before the call to the gold linker.
I’m
>> looking to get people’s feedback on whether there would be an
advantage to
>> waiting to run a number of these passes until the linking stage. For
>> example, I believe I saw a post a little while back about postponing
>> vectorization until the linking stage. It seems to me that there could
be
>> an advantage to postponing (some) passes until the linking stage, where
the
>> entire graph is available. In general, what do people think about the
idea
>> of a different flow of LTO where more passes are postponed until the
>> linking stage?
>>
>>
>>
>> Daniel Stewart
>>
>>
>>
>> --
>>
>> Qualcomm Innovation Center, Inc. is a member of Code Aurora Forum,
hosted
>> by The Linux Foundation
>>
>>
>>
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>>
>>